Island of Tomorrow (current story: The Notion)

"Physics, I can take you to a place."
 
Nothing was said as we sailed to the island, ported, and then slowly climbed the mountainous slope.
 
We went into a cave and walked about half a mile coming to the cave exit on the other side.
 
"I've seen this," I told Rock.
 

 
"I know you're thinking it is the cave glitch phenomenon."
 
"Yep."
 
"Normally you would be right--but it isn't.  Anyone coming here is gonna think they know what it is and turn around and go back.  We've seen that happen several time, from our vantage point on the other side."
 
"Wow!"
 
"Once you walk through it there are several rooms.  It isn't what it is entirely on its own, we did some stuff to make it was it is now, but not everything there is our technology.  We found some stuff.  Isaac Newton has come here three times.
 
"So, what is this place about?"
 
"Three things," D-Rock smiled.  "Infinity.  The infinitely small.  The end of time."
 
(to be continued soon...)

Woot! I love it! But such a tease, more please?

Ready for more!!!

D-Rock had promised to tell me what Newton had told him was the first thing to learn in logic.


"The word implies, in logic, is much stronger than how we use it normally."

"If I am talking in logic and I say that A implies B, there is no question, no hesitancy--with no exception having A be true implies that B is true.  For example, if the stoplight is green, I must drive through it.  We word things funny so that we can put them into logical games.

A=The stoplight is Green.
B=I must drive through the stoplight.

There is another, if and only if, but we delay that a bit.

Back to implies, we represent it with an arrow pointing to the right.

A --> B.


A=The pirate is a Fury pirate.
B=When the pirate fights, the pirate beasts!!!



Now, every time we see a pirate fighting, if the pirate is a Fury pirate we know the pirate is beasting!!!

There are three other situations to consider.

If the pirate is not beasting, the fighting pirate cannot be a Fury pirate.

If the pirate is beasting, we don't know whether or not they are a Fury pirate.

If the pirate is not a Fury pirate, we don't know whether or not they are beasting.





Now, for if and only if.  It is represented with arrows pointing two ways.  This choice will soon make sense.


What if we know B --> A?  That translates, what if only Fury pirates beasted, so if a pirate was beasting we knew the pirate was a fury pirate, because only Fury pirates beast?

"Wait!" I tell D-Rock.  "I disagree with that!  I have several friends outside of the Fury who beast all the time!"

"And you think I don't?"  D-Rock laughs.  "No, that's fine.  One thing we do, we consider premises and statements which we believe are false but we still try them anyway, to see where the argument leads.  This is part of thinking outside the box.   If pigs could fly how fast would  they fly?  Now back to the logic."

We have two statements now:

A --> B
B --> A

We put them together as  A <--> B.  Do you see the two arrows in the one arrow?

We can write this as A pirate is a Fury pirate if and only if the pirate is beasting when the pirate fights.  Note: given the statements, if several students translate it to English on a test, they won't use the exact same wording so we sometimes say we are stating it roughly.  You are a pirate--you like it rough, right?

To the Wall
 
Reliz took the ball and threw it at the wall.  It bounced back.
 
A dozen pirates cheered, and then each took a swig of rum.
 
“What is she doing?” Micy asked D-Rock.
 
“She’s making sure the ball bounces back.  As you can see, it did.”
 
“Well, the ball will always bounce back.”
 
“Are you sure?”
 
“Uh,” pause, “yeah…”
 
“Good.  So far it has worked every time.  Now, here’s the trick.  She is standing twelve feet from the wall.  It takes time for the ball to go halfway, to the point of six feet.  After that, it takes more time to go to the next halfway point, three feet.  After that one and half feet and it takes some time for that.  Always, it takes time to get to the next halfway point.  There is always another halfway point—and yet the ball reaches the wall and it doesn’t seem to have any trouble doing so.”

“So, what’s the trick?”

“There is something in those waters,” D-Rock said.  “Some call it a paradox, but I say it is like a Kracken of sorts.  We work very carefully when we come upon one of these.  What happens is, those halfway distances get incredibly small.  Now, we have found we can pack an infinite number of lengths into a finite distance.  The distance from Reliz to the wall is 12 feet and that is quite finite.  In another game we can pack an infinite number of triangles into a finite area.
 
(to be continued)


My fallible memory says the above story is a variation of “Archimedes and the Tortoise”.

The idea of  there always being a halfway point between two locations is an axiom in mathematics.  In fact, if we are working on a number line with points ‘a’ and ‘c’, we calculate the halfway point using the formula (a+b)/2.  To quickly show this, you know six is halfway between five and seven:  (5+7)/2=12/2=6.

The Notion
 
“Here’s my take on it,” D-Rock says. “You may try to explain something, and it isn’t easy, and before you finish the other pirate says, I get it.  What happened was, you transferred a notion.  Our ideas and the things we say may be built over notions.”
 
Sheriff walks up to D-Rock.  “D, I want to try making something on a ship that has metal cannon balls rolling back and forth counter to the listing of the ship.  It should reduce the list, but of course, it won’t take it away completely.”
 
“What’s the basic idea?”
 
“Well, the cannonballs provide weight on the side that is listing, so they work to push it back down.  Overall the idea is negative feedback—it dampens a phenomenon.”
 
“Is there a positive feedback?”
 
“Yes.  Positive feedback is bad.  If something starts moving and there is positive feedback, the positive feedback would make it go faster, and as it went faster, there would be more feedback, and the feedback would make it go faster…”
 
“Why cannonballs?”
 
“Well, sir, this thing depends on weight to work.  I didn’t want to add any weight to the ship so I needed to use something round and heavy that was already here and would be used for something else."  
 
"Sheriff, again, you are a genius.  You are going to be careful, right?”
 
“Yes.  So you’re give me some funding for the iron and to get the tracks built?”
 
“Sure!  I want a full report of everything that crosses your mind while you work it.”
 
 
Months later Sheriff is putting down the metal rails.
 
“Everything O.K. Sheriff?”
 
Sheriff is too busy working and didn’t hear the question.  D-Rock lets him continue and a few pirates who see what happens quietly smile.
 
“I like diligence,” D-Rock says.  Sheriff doesn’t hear that either.
 
D-Rock pulls out a piece of paper that had a transparent wax covering both sides.
 
“This is important.  I thought about trying to put it into words but then I decided to instead draw the picture and show a list of some numbers.  There is a type of thinking that your brain does, and as you look at the pictures and the numbers you will try to ascribe meaning to it.  Also, I’m not asking any pirate to see everything the first time you look at it.  Take your time.  You might think of stuff later when you aren’t looking at it.  I want to encourage that kind of discovery.”


 

 


“Interesting…” You tell D-Rock.
 
“So I’d like to know if, you get the notion,” D-Rock says.
 
Suddenly the ship lists to the right, hard!
 
Yells of pirates are heard.
 
Then the ship lists to the left, even harder!
 
“DON’T ROCK THE BOAT, SHERIFF!” Angel Fury yells in upper case.
 
The ship listed even harder to the right!
 
“DON’T TIP THE BOAT OVER!” Nate hollers in double upper case.
 
The sound of cannon balls hitting the deck with a thud was heard as Sheriff pushes them off the tracks. The ship returns to the normal list.
 
“Everyone, O.K?” D-Rock asks.
 
“I think our cat is traumatized, but everyone else seems all right,” Paula answers.